sin(x)^2+cos(x)^2 = 1 on different calcs

[Albert Chan]

(09-25-2018 05:19 AM)Joe Horn Wrote:  Dieter is right. Besides, the 30S isn't really an HP calculator. It's a rebranded knockoff of somebody else's calculator.
Proof: do 1/3, then Ans×3, then Ans-1. It returns zero, which proves it's cheating by fudging results.

Agreed. Many (most?) calculators cheat, to give "nice" answer.
They call this "small differences set to zero feature" ... I hate it

I am not sure about the proof though. IIRC, 30S use binary mathematics:

1/3 = 0.010101011 (binary, say 8 bits mantissa)
2/3 = 0.10101011
3/3 = 1.000000001 -> half-way round-to-even = 1.0

1/3 = 0.01010101 (binary, say 7 bits mantissa)
2/3 = 0.1010101
3/3 = 0.11111111 -> half-way round-to-even = 1.0

So, whatever bits 30S uses (odd or even), 1/3*3 = 1, no cheating (in this case)